That's exactly what's happened. And it's also weird for me, because if Blender can recognize that the file's (original video clip) name has change, then I want to know how it does it. No other program does that.
But, when I group the video strip with another video strip or an audio strip, then it doesn't recognize it (before I change the strip's path).
Even if the first part is a coincidence, then why not make it work for sure?